Group #14298414 — subgroups

Subgroups — #14298414

Order 1920.

544 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91815	C₂	1	1	yes	maximal, characteristic
2	C₅×#5207	C₂	1	1	yes	maximal, characteristic
3	C₃×#65496	C₂	1	1	yes	maximal, characteristic
4	#11745987	C₂	1	4	yes	maximal, complemented
5	#10600767	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×#6719	C₄	1	2	yes	—
8	#91815	—	2	2	no	—
9	#91815	—	2	2	no	—
10	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
11	C₂×C₄×Dic₁₅	C₄	1	2	yes	—
12	C₂×C₅×#208	C₂²	1	2	yes	—
13	C₂×C₃×#681	C₂²	1	2	yes	—
14	C₅×#830	—	2	2	no	—
15	C₃×C₂²⋊#168	—	2	2	no	—
16	#69974	—	5	1	no	maximal, Hall
17	C₂×#4072	—	3	1	no	—
18	C₅×#407	—	3	1	no	—
19	#65496	D₃	1	1	yes	characteristic
20	#64774	—	3	4	no	—
21	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₃×C₄×C₅	—	2	4	no	—
23	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
25	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
26	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₅	C₂×C₄	1	4	yes	—
28	#6719	—	2	4	no	—
29	C₄⋊Dic₁₅	—	2	2	no	—
30	C₄⋊Dic₁₅	—	2	2	no	—
31	C₄×Dic₁₅	—	2	4	no	—
32	C₅×#208	—	2	4	no	—
33	C₂×C₅×C₃⋊C₈	—	2	2	no	—
34	C₃×#681	—	2	4	no	—
35	C₂×C₃×#168	—	2	2	no	—
36	C₂×#926	—	5	1	no	—
37	C₃×#407	—	5	1	no	—
38	#5207	D₅	1	1	yes	characteristic
39	#4554	—	5	4	no	—
40	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
41	C₂×C₅×M₁₆	—	3	2	no	—
42	C₂×C₂²⋊Dic₅	—	3	2	no	—
43	#4072	—	6	2	no	—
44	#4072	—	6	2	no	—
45	C₂×C₄⋊Dic₅	—	3	2	no	—
46	C₂×C₄×Dic₅	—	3	2	no	—
47	C₂×#681	C₂×D₃	1	2	yes	—
48	C₅×C₂²⋊C₈	—	6	2	no	—
49	C₂²⋊#168	—	2	2	no	—
50	#1822	—	15	1	no	Sylow
51	C₂³×C₃×C₅	—	2	2	no	—
52	C₂³×C₃×C₅	—	4	2	no	—
53	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
54	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₃×C₄×C₅	—	2	4	no	—
57	C₂×C₃×C₄×C₅	—	2	4	no	—
58	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
59	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
60	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
61	C₂×C₃×C₄×C₅	#41	1	4	yes	—
62	C₂×Dic₁₅	—	2	4	no	—
63	C₂×Dic₁₅	—	4	4	no	—
64	C₃×#168	—	4	2	no	—
65	C₅×C₃⋊C₈	—	4	2	no	—
66	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
67	C₂×C₃×M₁₆	—	5	2	no	—
68	C₂×#217	—	5	2	no	—
69	#926	—	10	2	no	—
70	#926	—	10	2	no	—
71	C₂×C₄⋊Dic₃	—	5	2	no	—
72	C₂×C₄×Dic₃	—	5	2	no	—
73	C₂×#208	C₂×D₅	1	2	yes	—
74	C₃×C₂²⋊C₈	—	10	2	no	—
75	#830	—	2	2	no	—
76	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
77	C₂²×C₄×C₅	—	2	4	no	—
78	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
79	C₂²×C₄×C₅	D₁₂	1	2	yes	—
80	C₂²×C₄×C₅	#67	1	2	yes	—
81	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
82	C₂²×Dic₅	—	3	4	no	—
83	C₅×M₁₆	—	6	4	no	—
84	C₂×C₅×C₈	—	6	2	no	—
85	C₂²⋊Dic₅	—	6	4	no	—
86	C₄⋊Dic₅	—	6	2	no	—
87	C₄⋊Dic₅	—	6	2	no	—
88	C₄×Dic₅	—	6	4	no	—
89	#681	—	2	4	no	—
90	C₂×#168	—	2	2	no	—
91	C₂×#117	—	15	1	no	—
92	#407	—	3	1	no	—
93	#407	—	5	1	no	—
94	#343	—	15	4	no	—
95	C₂²×C₃×C₅	—	2	2	no	—
96	C₂²×C₃×C₅	—	2	2	no	—
97	C₂²×C₃×C₅	—	2	4	no	—
98	C₂²×C₃×C₅	—	4	4	no	—
99	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₃×C₅	#117	1	2	yes	—
101	C₃×C₄×C₅	—	2	2	no	—
102	C₃×C₄×C₅	#123	1	2	yes	—
103	C₃×C₄×C₅	#123	1	2	yes	—
104	Dic₁₅	—	4	4	no	—
105	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
106	C₂²×C₃×C₄	—	2	4	no	—
107	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
108	C₂²×C₃×C₄	D₂₀	1	2	yes	—
109	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
110	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
111	C₂²×Dic₃	—	5	4	no	—
112	C₃×M₁₆	—	10	4	no	—
113	C₂×C₃×C₈	—	10	2	no	—
114	#217	—	10	4	no	—
115	C₄⋊Dic₃	—	10	2	no	—
116	C₄⋊Dic₃	—	10	2	no	—
117	C₄×Dic₃	—	10	4	no	—
118	#208	—	2	4	no	—
119	C₂×C₃⋊C₈	—	2	2	no	—
120	C₂³×C₅	—	2	2	no	—
121	C₂³×C₅	—	4	2	no	—
122	C₂³×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
123	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
124	C₂×C₄×C₅	—	2	2	no	—
125	C₂×C₄×C₅	—	2	4	no	—
126	C₂×C₄×C₅	—	2	4	no	—
127	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
128	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
129	C₂×C₄×C₅	#237	1	4	yes	—
130	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
131	C₂×Dic₅	—	6	4	no	—
132	C₂×Dic₅	—	12	4	no	—
133	C₅×C₈	—	12	2	no	—
134	#168	—	4	2	no	—
135	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
136	C₂×M₁₆	—	3	2	no	—
137	C₂×M₁₆	—	5	2	no	—
138	#117	—	30	2	no	—
139	#117	—	30	2	no	—
140	C₂×C₄⋊C₄	—	15	2	no	—
141	C₂×C₂²⋊C₄	—	15	2	no	—
142	C₂×C₄²	—	15	2	no	—
143	C₂²⋊C₈	—	6	2	no	—
144	C₂²⋊C₈	—	10	2	no	—
145	C₂×C₃×C₅	—	2	2	no	—
146	C₂×C₃×C₅	—	4	2	no	—
147	C₂×C₃×C₅	#381	1	1	yes	characteristic
148	C₂×C₃×C₅	#413	1	2	yes	—
149	C₂³×C₃	—	2	2	no	—
150	C₂³×C₃	—	4	2	no	—
151	C₂³×C₃	#685	1	2	yes	—
152	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
153	C₂×C₃×C₄	—	2	2	no	—
154	C₂×C₃×C₄	—	2	4	no	—
155	C₂×C₃×C₄	—	2	4	no	—
156	C₂×C₃×C₄	#685	1	2	yes	—
157	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
158	C₂×C₃×C₄	#711	1	4	yes	—
159	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
160	C₂×Dic₃	—	10	4	no	—
161	C₂×Dic₃	—	20	4	no	—
162	C₃×C₈	—	20	2	no	—
163	C₃⋊C₈	—	4	2	no	—
164	C₂²×C₅	—	2	2	no	—
165	C₂²×C₅	—	2	4	no	—
166	C₂²×C₅	—	2	2	no	—
167	C₂²×C₅	—	4	4	no	—
168	C₂²×C₅	#877	1	2	yes	—
169	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
170	C₄×C₅	—	2	2	no	—
171	C₄×C₅	#886	1	2	yes	—
172	C₄×C₅	#935	1	2	yes	—
173	Dic₅	—	12	4	no	—
174	C₂⁴	#1200	1	1	yes	characteristic
175	C₂²×C₄	—	2	4	no	—
176	C₂²×C₄	—	15	4	no	—
177	C₂²×C₄	#1200	1	1	yes	characteristic
178	C₂²×C₄	#1202	1	2	yes	—
179	C₂²×C₄	#1203	1	2	yes	—
180	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
181	M₁₆	—	6	4	no	—
182	M₁₆	—	10	4	no	—
183	C₂×C₈	—	6	2	no	—
184	C₂×C₈	—	10	2	no	—
185	C₄⋊C₄	—	30	2	no	—
186	C₄⋊C₄	—	30	2	no	—
187	C₂²⋊C₄	—	30	4	no	—
188	C₄²	—	30	4	no	—
189	C₃×C₅	#1822	1	1	yes	characteristic, complemented, Hall
190	C₂²×C₃	—	2	2	no	—
191	C₂²×C₃	—	2	4	no	—
192	C₂²×C₃	—	2	2	no	—
193	C₂²×C₃	—	4	4	no	—
194	C₂²×C₃	#4023	1	2	yes	—
195	C₂²×C₃	C₂×#685	1	1	yes	characteristic
196	C₃×C₄	—	2	2	no	—
197	C₃×C₄	#4032	1	2	yes	—
198	C₃×C₄	#4081	1	2	yes	—
199	Dic₃	—	20	4	no	—
200	C₂×C₅	—	2	2	no	—
201	C₂×C₅	—	4	2	no	—
202	C₂×C₅	#4943	1	1	yes	characteristic
203	C₂×C₅	#5132	1	2	yes	—
204	C₂³	—	2	2	no	—
205	C₂³	—	4	2	no	—
206	C₂³	#6667	1	2	yes	—
207	C₂³	C₂×#1200	1	1	yes	characteristic
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	30	4	no	—
212	C₂×C₄	—	60	4	no	—
213	C₂×C₄	#6667	1	2	yes	—
214	C₂×C₄	#6780	1	4	yes	—
215	C₂×C₄	C₂×#1202	1	1	yes	characteristic
216	C₂×C₄	C₂×#1203	1	1	yes	characteristic
217	C₈	—	12	2	no	—
218	C₈	—	20	2	no	—
219	C₂×C₃	—	2	2	no	—
220	C₂×C₃	—	4	2	no	—
221	C₂×C₃	#65232	1	1	yes	characteristic
222	C₂×C₃	#65421	1	2	yes	—
223	C₅	#69974	1	1	yes	characteristic, complemented, Sylow
224	C₂²	—	2	2	no	—
225	C₂²	—	2	4	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	4	4	no	—
228	C₂²	#91532	1	2	yes	—
229	C₂²	C₂×#6667	1	1	yes	characteristic
230	C₄	—	2	2	no	—
231	C₄	—	60	4	no	—
232	C₄	#91537	1	2	yes	—
233	C₄	#91543	1	2	yes	—
234	C₃	#10600767	1	1	yes	characteristic, complemented, Sylow
235	C₂	—	2	2	no	—
236	C₂	—	4	2	no	—
237	C₂	#11748357	1	2	yes	—
238	C₂	#11749473	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#91815

C₂

yes

maximal, characteristic

C₅×#5207

C₂

yes

maximal, characteristic

C₃×#65496

C₂

yes

maximal, characteristic

#11745987

C₂

yes

maximal, complemented

#10600767

—

maximal, Hall

C₂³×C₃×C₄×C₅

C₂²

yes

characteristic

C₂×#6719

C₄

yes

—

#91815

—

#91815

—

C₂×C₄⋊Dic₁₅

C₂²

yes

—

C₂×C₄×Dic₁₅

C₄

yes

—

C₂×C₅×#208

C₂²

yes

—

C₂×C₃×#681

C₂²

yes

—

C₅×#830

—

C₃×C₂²⋊#168

—

—

—

—

D₃

yes

characteristic

#64774

—

C₂⁴×C₃×C₅

C₂×C₄

yes

characteristic

C₂²×C₃×C₄×C₅

—

C₂²×C₃×C₄×C₅

C₂×C₄

yes

characteristic

C₂²×C₃×C₄×C₅

D₄

yes

—

C₂²×C₃×C₄×C₅

D₄

yes

—

C₂²×C₃×C₄×C₅

C₂³

yes

characteristic

C₂²×Dic₁₅

C₂×C₄

yes

—

#6719

—

C₄⋊Dic₁₅

—

C₄⋊Dic₁₅

—

C₄×Dic₁₅

—

C₅×#208

—

C₂×C₅×C₃⋊C₈

—

C₃×#681

—

C₂×C₃×#168

—

C₂×#926

—

C₃×#407

—

#5207

D₅

yes

characteristic

#4554

—

C₂³×C₄×C₅

C₂×D₃

yes

characteristic

C₂×C₅×M₁₆

—

C₂×C₂²⋊Dic₅

—

#4072

—

#4072

—

C₂×C₄⋊Dic₅

—

C₂×C₄×Dic₅

—

C₂×#681

C₂×D₃

yes

—

C₅×C₂²⋊C₈

—

C₂²⋊#168

—

#1822

—

Sylow

C₂³×C₃×C₅

—

C₂³×C₃×C₅

—

C₂³×C₃×C₅

C₂²⋊C₄

yes

—

C₂³×C₃×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

C₂²⋊C₄

yes

—

C₂×C₃×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₃×C₄×C₅

#41

yes

—

C₂×Dic₁₅

—

C₂×Dic₁₅

—

C₃×#168

—

C₅×C₃⋊C₈

—

C₂³×C₃×C₄

C₂×D₅

yes

characteristic

C₂×C₃×M₁₆

—

C₂×#217

—

#926

—

#926

—

C₂×C₄⋊Dic₃

—

C₂×C₄×Dic₃

—

C₂×#208

C₂×D₅

yes

—

C₃×C₂²⋊C₈

—

#830

—

C₂⁴×C₅

C₄×D₃

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₄×D₃

yes

characteristic

C₂²×C₄×C₅

D₁₂

yes

—

C₂²×C₄×C₅

#67

yes

—

C₂²×C₄×C₅

C₂²×D₃

yes

characteristic

C₂²×Dic₅

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂²⋊Dic₅

—

C₄⋊Dic₅

—

C₄⋊Dic₅

—

C₄×Dic₅

—

—

—

—

—

—

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

C₂×C₂²⋊C₄

yes

characteristic

100

C₂²×C₃×C₅

#117

yes

—

101

C₃×C₄×C₅

—

102

C₃×C₄×C₅

#123

yes

—

103

C₃×C₄×C₅

#123

yes

—

104

Dic₁₅

—

105

C₂⁴×C₃

C₄×D₅

yes

characteristic

106

C₂²×C₃×C₄

—

107

C₂²×C₃×C₄

C₄×D₅

yes

characteristic

108

C₂²×C₃×C₄

D₂₀

yes

—

109

C₂²×C₃×C₄

C₂²⋊D₅

yes

—

110

C₂²×C₃×C₄

C₂²×D₅

yes

characteristic

111

C₂²×Dic₃

—

112

C₃×M₁₆

—

113

C₂×C₃×C₈

—

114

#217

—

115

C₄⋊Dic₃

—

116

C₄⋊Dic₃

—

117

C₄×Dic₃

—

118

#208

—

119

C₂×C₃⋊C₈

—

120

C₂³×C₅

—

121

C₂³×C₅

—

122

C₂³×C₅

(C₂×D₃)⋊C₄

yes

—

123

C₂³×C₅

C₂×C₄×D₃

yes

characteristic

124

C₂×C₄×C₅

—

125

C₂×C₄×C₅

—

126

C₂×C₄×C₅

—

127

C₂×C₄×C₅

(C₂×D₃)⋊C₄

yes

—

128

C₂×C₄×C₅

C₂×D₁₂

yes

characteristic

129

C₂×C₄×C₅

#237

yes

—

130

C₂×C₄×C₅

C₂×#67

yes

characteristic

131

C₂×Dic₅

—

132

C₂×Dic₅

—

133

C₅×C₈

—

134

#168

—

135

C₂³×C₄

D₃×D₅

yes

characteristic

136

C₂×M₁₆

—

137

C₂×M₁₆

—

138

#117

—

139

#117

—

140

C₂×C₄⋊C₄

—

141

C₂×C₂²⋊C₄

—

142

C₂×C₄²

—

143

C₂²⋊C₈

—

144

C₂²⋊C₈

—

145

C₂×C₃×C₅

—

146

C₂×C₃×C₅

—

147

C₂×C₃×C₅

#381

yes

characteristic

148

C₂×C₃×C₅

#413

yes

—

149

C₂³×C₃

—

150

C₂³×C₃

—

151

C₂³×C₃

#685

yes

—

152

C₂³×C₃

C₂×C₄×D₅

yes

characteristic

153

C₂×C₃×C₄

—

154

C₂×C₃×C₄

—

155

C₂×C₃×C₄

—

156

C₂×C₃×C₄

#685

yes

—

157

C₂×C₃×C₄

C₂×D₂₀

yes

characteristic

158

C₂×C₃×C₄

#711

yes

—

159

C₂×C₃×C₄

C₂×C₂²⋊D₅

yes

characteristic

160

C₂×Dic₃

—

161

C₂×Dic₃

—

162

C₃×C₈

—

163

C₃⋊C₈

—

164

C₂²×C₅

—

165

C₂²×C₅

—

166

C₂²×C₅

—

167

C₂²×C₅

—

168

C₂²×C₅

#877

yes

—

169

C₂²×C₅

C₂×(C₂×D₃)⋊C₄

yes

characteristic

170

C₄×C₅

—

171

C₄×C₅

#886

yes

—

172

C₄×C₅

#935

yes

—

173

Dic₅

—

174

C₂⁴

#1200

yes

characteristic

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

#1200

yes

characteristic

178

C₂²×C₄

#1202

yes

—

179

C₂²×C₄

#1203

yes

—

180

C₂²×C₄

C₂×D₃×D₅

yes

characteristic

181

M₁₆

—

182

M₁₆

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₄²

—

189

C₃×C₅

#1822

yes

characteristic, complemented, Hall

190

C₂²×C₃

—

191

C₂²×C₃

—

192

C₂²×C₃

—

193

C₂²×C₃

—

194

C₂²×C₃

#4023

yes

—

195

C₂²×C₃

C₂×#685

yes

characteristic

196

C₃×C₄

—

197

C₃×C₄

#4032

yes

—

198

C₃×C₄

#4081

yes

—

199

Dic₃

—

200

C₂×C₅

—

201

C₂×C₅

—

202

C₂×C₅

#4943

yes

characteristic

203

C₂×C₅

#5132

yes

—

204

C₂³

—

205

C₂³

—

206

C₂³

#6667

yes

—

207

C₂³

C₂×#1200

yes

characteristic

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

#6667

yes

—

214

C₂×C₄

#6780

yes

—

215

C₂×C₄

C₂×#1202

yes

characteristic

216

C₂×C₄

C₂×#1203

yes

characteristic

217

C₈

—

218

C₈

—

219

C₂×C₃

—

220

C₂×C₃

—

221

C₂×C₃

#65232

yes

characteristic

222

C₂×C₃

#65421

yes

—

223

C₅

#69974

yes

characteristic, complemented, Sylow

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

#91532

yes

—

229

C₂²

C₂×#6667

yes

characteristic

230

C₄

—

231

C₄

—

232

C₄

#91537

yes

—

233

C₄

#91543

yes

—

234

C₃

#10600767

yes

characteristic, complemented, Sylow

235

C₂

—

236

C₂

—

237

C₂

#11748357

yes

—

238

C₂

#11749473

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#6667
commutator	C₂³×C₃×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	#1822
LCS	G ▷ C₂³×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂³×C₄

subgroup

G/H

center

C₂²

C₂×#6667

commutator

C₂³×C₃×C₅

C₂²×C₄

Frattini

C₂²×C₄

C₂×D₃×D₅

Fitting

C₂³×C₃×C₄×C₅

C₂²

socle

C₂²×C₃×C₅

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₃×C₅

C₂×C₄

cosocle

C₂²×C₃×C₄×C₅

C₂³

hypercenter

C₂³×C₄

D₃×D₅

hypocenter

C₃×C₅

#1822

LCS

G ▷ C₂³×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂² ◁ C₂³×C₄

N	H ≅ G/N	type
4. #11745987	C₂	semidirect
189. C₃×C₅	#1822	semidirect
223. C₅	#69974	semidirect
234. C₃	#10600767	semidirect

H ≅ G/N

type

4. #11745987

C₂

semidirect

189. C₃×C₅

#1822

semidirect

223. C₅

#69974

semidirect

234. C₃

#10600767

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#91815	2
C₅×#5207	2
C₃×#65496	2
#11745987	2
#10600767	3
#69974	5

subgroup

index

Subgroups — #14298414

Conjugacy classes of subgroups

Complements

Maximal subgroups